Steganalysis Secret Message Using Rich Model Method for Stego Color Image

As communication and internet technologies have advanced, a significant volume of images is shared via public networks. Has recently been discovered that a large number of criminal organizations use images to distribute their illegal data. These organizations use images to hide their harmful data [1]. They typically use steganography techniques for hiding their dangerous material within images [2]. As a result, scientists have begun using steganalysis models to identify images with embedded data. Therefore, one method for identifying data hidden in images is image steganalysis. As a result, steganalysis determines if the provided image is a normal image or a stego-embedded one [3].

Embedding hidden messages into an image such that only the intended recipients can recognize them is the aim of image steganography. It can be used to integrate patient data into medical images, personal information into smart ID (identification card) photos, and copyright information into professional images [4]. Image steganalysis is a technique used to try and find hidden messages in images [5]. As image steganography has advanced, numerous steganalysis techniques have been created to address these new developments [6]. Early on, it is presumed that some knowledge of steganographic algorithms that embed a secret message into images is already known [7]. We refer to this as targeted steganalysis, but in recent years, a more likely scenario has received greater attention. In other words, there is no knowledge about steganographic algorithms [8]. Blind steganalysis is the process of attempting to distinguish between stego and cover images without being knowledgeable about steganographic embedding approaches [9]. We can create a classifier that distinguishes between cover and stego images in the feature space by using features taken from a training set of cover and stego images [10].

However, many existing steganalysis methods suffer from critical limitations. These include poor performance when dealing with high-resolution or color images, low generalization across various steganographic algorithms, and vulnerability to adaptive or content-aware embedding techniques that minimize detectable traces. Furthermore, traditional methods often rely on handcrafted features, which may not adequately capture the subtle statistical differences caused by data embedding. To address these challenges, the proposed method utilizes the Rich Model framework, which extracts high-dimensional statistical features and captures pixel-level intensity differences across color channels. This approach enables more accurate detection of hidden messages.

In 2020, Mohamed et al. [11] discussed how Deep Learning algorithms have outperformed conventional techniques in both the spatial and transform domains when used in steganalysis. Even better results have been achieved when steganalysis utilizing Deep Learning is combined with manual feature extraction and classification phases. Since this field is still developing and the initial results are encouraging, the authors suggest working on image steganalysis using deep learning.

In 2020, Xu [12] proposed the technique outperforms the One-class SVM methodology for anomaly identification and for both steganographic and non-steganographic texts, the Type-1 Model’s results demonstrate good precision, recall and F1-measure scores. Additionally, the LSTM and BI-LSTM models show strong text steganalysis precision, recall, and F1 measure scores. Thus, without the need for human interaction, the unsupervised deep learning method successfully detects text steganography in a completely unsupervised approach.

In 2021, Yamini et al. [13] proposed an adaptive image steganalysis system that used the support vector machine (SVM) classifier, achieving a 96.72% classification accuracy. As a result, the enhanced canny edge detection algorithm was selected for edge recognition in the suggested system after outperforming other segmentation algorithms.

In 2021, You et al. [14] proposed an innovative, deep learning, end-to-end method that delivers satisfactory performance for separating steganography images from original images. When producing the final classification based on the relationships between the noise of various image sub-regions, the suggested network first accepts the image as input. Preprocessing, feature extraction, and fusion/classification are the three steps of the algorithm’s Siamese CNN-based architecture, which comprises two symmetrical subnets with common parameters. Generated datasets that included steganography images in various sizes and the equivalent normal images from BOSS-base 1.01 and ALASKA were used to validate the network. Our suggested network is flexible and well-generalized, according to experimental results derived from data collected through several methods.

In 2022, Vilkhovskiy [15] proposed that the algorithm utilized in the study can identify an area with a high density of unique pixel combinations and locate an LSB-insert and its location due to the steganalysis approach that was proposed and demonstrated in the study to have high detection and locating accuracy in a low stego payload of 25/10. Thus, LSB inserts in low stego-payload fake color images are successfully detected and located by the provided method.

The Rich Model is a high-dimensional feature extraction technique used in steganalysis to capture subtle embedding artifacts in digital images. It operates by applying a variety of high-pass filters to the image to compute residuals that emphasize the noise-like patterns introduced by data hiding processes. These residuals are then used to build co-occurrence matrices that reflect the statistical dependencies between neighboring pixel values.

In the case of color images, the Rich Model is extended to consider inter-channel correlations, such as differences between the red, green, and blue channels (e.g., R-G, G-B). This adaptation allows the model to capture complex embedding traces that may vary across different color components. These residuals are then used to extract higher-order co-occurrence features that capture complex statistical dependencies within the image. The resulting feature set, which can include tens of thousands of descriptors, provides a detailed representation of the image’s structural patterns. These features are subsequently fed into a machine learning classifier—such as ensemble-based methods—to determine the presence or absence of hidden information.

By capturing complex dependencies in digital images, especially in color images where inter-channel interactions are intricate, rich models have significantly enhanced steganalysis. These techniques improve the detection of hidden information by extracting high-dimensional feature sets that represent different statistical features of images [19].

Three-dimensional co-occurrences of residuals calculated from all three color channels were introduced in one important application of the spatial rich model to color images. This method improved detection capabilities, particularly for images that included color interpolation artifacts, by successfully capturing dependencies across color channels. Researchers have improved rich models for color image steganalysis by building on this foundation. One method, for instance, was to use co-occurrences of color noise residuals that were divided based on the Bayer color filter array’s structure. By taking into consideration the unique features of color image acquisition, this technique aims to enhance detection [20]. Rs analysis integrates a statistical study of the pixel positions where modifications happen with a steganalysis grounded in the Image fidelity metrics. Steganalysis based on image type or embedding method includes the examination of images—such as those in JPEG format—to identify hidden content, it allso includes methods for revealing hidden messages in stego images generated by steganography tools when the embedding algorithm is known. By analyzing selected features from image, artifact detection systems offer techniques to identify differences between the original and steganographic images [21].

Steganalysis is the process of examining digital content, such images, to find hidden messages. A high-dimensional feature set obtained from an image’s statistical and spatial properties is used by the rich model, a complete framework. Equations and applications are included in this thorough presentation of the main ideas [24].

5.1 Mean intensity ( $\mu$ )

The mean intensity represents the average brightness of all pixel values in an image. It provides a baseline to identify anomalies embedding process. For a grayscale image with pixel intensities ranging from 0 to 255:

$\mu=\frac{1}{N} \sum_{i=1}^N I_i$ (6)

where,

• $N$ is the total number of pixels.
• $I_i$ is the intensity of the $i$-th pixel.

Application: the mean intensity may change somewhat to facilitate identification if embedding changes pixel values in the manner that is desired.

5.2 Standard deviation of intensity ($\sigma$)

The standard deviation highlights variances by calculating the distribution of pixel values around the mean. It is computed as follows:

$\sigma=\sqrt{\frac{1}{N} \sum_{i=1}^N\left(I_i-\mu\right)^2}$  (7)

Application: local pixel values are frequently changed by embedding, increasing or decreasing intensity variations that can be identified by changes in $\sigma$.

5.3 Skewness of intensity

The asymmetry of the pixel intensity distribution is measured by skewness. A tail on the right (greater intensity values) is indicative of positive skewness, and a tail on the left is indicative of negative skewness.

Skewness $=\frac{\frac{1}{N} \sum_{i=1}^N\left(I_i-\mu\right)^3}{\sigma^3}$   (8)

Application: skewness is a crucial metric since many steganographic techniques try to prevent symmetry in embedding.

5.4 Kurtosis of intensity

Kurtosis quantifies the intensity distribution’s “tailenderss” or peak sharpness. The calculation for excess kurtosis is:

Kurtosis $=\frac{\frac{1}{N} \sum_{i=1}^N\left(I_i-\mu\right)^4}{\sigma^4}-3$    (9)

Application: unusual pixel value clustering brought on by embedding may be indicated by abnormal kurtosis values.

5.5 Third moment of intensity ($M_3$)

The third moment generates an unnormalized measure of asymmetry, helping detect small distribution changes:

$M_3=\frac{1}{N} \sum_{i=1}^N\left(I_i-\mu\right)^3$    (10)

5.6 Fourth moment of intensity ($M_4$)

An unnormalized indicator of distribution “peakedness” or flatness is given by the fourth moment:

$M_4=\frac{1}{N} \sum_{i=1}^N\left(I_i-\mu\right)^4$   (11)

5.7 Percentiles of intensity

Percentiles are useful for tracking localized changes in intensity because they separate the data into different ranges. For instance:

• $P_{25}$: 25th percentile (lower quartile)
• $P_{50}$: Median
• $P_{75}$: Upper quartile

Application: percentiles offer reliable measurements that are not impacted by extreme outliers [25].

This section presents all experimental evaluations conducted on stego color images and the retrieval of hidden messages. Table 1 displays a stego color image and its corresponding cover image. Table 2 presents a comparison of metrics between the stego-color image and the original cover image, including Information Entropy (IE), Mean Square Error (MSE), Correlation Coefficient, and Peak Signal-to-Noise Ratio (PSNR). Meanwhile, Table 3 displays the histogram analysis of both images. stego color image and the cover image. Table 4 shows the result of applying properties of the rich model on the stego color images, and Table 5 shows the result of applying properties of the rich model on color images without stego.

Table 1. Color imagr sans stego and stego-image

Name of Image	Stego-Color Image	Color Image without Stego
Cat	tu_pian_1.jpg	tu_pian_4.jpg
Butterfly	tu_pian_5.jpg	tu_pian_6.jpg
Bird	tu_pian_7.jpg	tu_pian_8.jpg
Wolf	tu_pian_9.jpg	tu_pian_10.jpg
Peacock	tu_pian_11.jpg	tu_pian_12.jpg

Table 2. Measures of, PSNR, information entropy, MSE and correlation coefficient

Table 3. Histogram comparing stego color image against one without

Image	Stego Color Image	Color Image without Stego
tu_pian_13.jpg	tu_pian_18.png	tu_pian_19.png
tu_pian_14.jpg	tu_pian_20.png	tu_pian_21.png
tu_pian_15.jpg	tu_pian_22.png	tu_pian_23.png
tu_pian_16.jpg	tu_pian_24.png	tu_pian_25.png
tu_pian_17.jpg	tu_pian_26.png	tu_pian_27.png

Table 4. Properties of rich model in the stego color images

Table 5. Properties of rich model on the color images without stego